We can solve for one variable in one of the equations and substitute the resulting expression into the other equation to obtain the value of the other variable.
From the second equation, we have:
x + 2y + 14 = 0
Solving for x, we get:
x = -2y - 14
Substituting this expression into the first equation, we get:
y = (-2y - 14)^2 + 3(-2y - 14) - 18
Expanding and simplifying, we have:
y = 4y^2 + 56y + 196
Bringing all terms to one side, we have:
4y^2 + 55y + 196 = 0
We can solve for y using the quadratic formula:
y = (-55 ± sqrt(55^2 - 4(4)(196))) / (2(4))
y = (-55 ± sqrt(1081)) / 8
y ≈ -4.31 or y ≈ -11.44
Substituting each value of y into the expression we found for x earlier, we have:
x = -2(-4.31) - 14 ≈ 6.62
x = -2(-11.44) - 14 ≈ 18.89
Therefore, the solutions to the system of equations are approximately (6.62, -4.31) and (18.89, -11.44).